Write the formula used to find the total surface area of a right circular cylinder.

We know that, A right circular cylinder is a three-dimensional solid shape that consists of two parallel bases linked by a closed circular surface where each base is like a circular disk in shape Total surface area of a right circular cylinder: It is defined as the area that is occupied by the entire cylinder. This area of cylinder consists of two circles and a curved surface. Then, Total surface area of a right circular cylinder = 2 π r h + 2 π r 2 = 2 π r h + r , where r is the radius of the cylinder and h is the height of cylinder.

The slant height of the frustum of a cone is 4 cm and the perimeter of its circular bases are 18 cm and 6 cm respectively. Find the curved surface area of the frustum.

Given, slant height of the frustum of a cone, l = 4 cm Circumference of the circular end = 18 cm ⇒ 2 × π r 1 = 18 cm ⇒ π r 1 = 9 _______________ 1 Circumference of the other circular end = 6 cm ⇒ 2 × π r 2 = 6 ⇒ π r 2 = 3 ________________ 2 Curved surface area of a frustum = π r 1 + π r 2 l , where r 1 and r 2 are the radii of the circular ends and l is the slant height Curved surface area of the frustum = 9 + 3 × 4 cm 2 = 48 cm 2 Therefore, the curved surface area of the frustum is 48 cm 2 .

A solid is in the form of a cone mounted on a right circular cylinder, both having same radii as shown in the figure. The radius of the base and height of the cone are 7 cm and 9 cm respectively. If the total height of the solid is 30 cm , find the volume of the solid.

Given, radius of the cylinder = 7 cm Height of the cylinder = 30 cm - 9 cm = 21 cm Volume of a cylinder = π r 2 h , where r is the radius of the cylinder and h is the height of the cylinder Volume of the cylinder = 22 7 × 7 cm 2 × 21 cm = 1029 cm 3 Radius of the cone = 7 cm Height of the cone = 9 cm Volume of a cone = 1 3 π r 2 h , where r is the radius of the cone and h is the height of the cone Volume of the cone = 1 3 × 22 7 × 7 cm 2 × 9 cm = 462 cm 3 Therefore, the volume of the solid = 462 cm 3 + 1029 cm 3 = 1491 cm 3 Hence, the required volume is 1491 cm 3 .

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Karnataka Board-2020>Q 11

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10th Karnataka Board

IMPORTANT

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Write the formula to find the total surface area of a right-circular cone whose circular base radius is $‘ r ’$ and slant height is $‘ l ’ .$

Important Questions on Surface Areas and Volumes

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10th Karnataka Board

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Karnataka Board-2020>Q 12

A medicine capsule is in the shape of cylinder with hemispheres stuck to each of its ends. The length of entire capsule is $14 mm$ and the diameter of the capsule is $5 mm$ . Find its surface area.

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10th Karnataka Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Surface Areas and Volumes>Karnataka Board-2020>Q 13

A right circular cone of height $30 cm$ is cut and removed by a plane parallel to its base from the vertex. If the volume of smaller cone obtained is $\frac{1}{27}$ of the volume of the given cone. Calculate the height of the remaining part of the cone.

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